# Thread: 4-regular Graph

1. ## 4-regular Graph

Prove there is precisely one 4 regular graph on 6 vertices.
any advice will help

2. I don't know if this will work but have you tried showing that any two 4-regular graph on 6 vertices are isomorphic?

3. Originally Posted by guildmage
I don't know if this will work but have you tried showing that any two 4-regular graph on 6 vertices are isomorphic?
well i tried to get 4,4,4,4,4,4 down to C4 and show that its unique subgraph and build my way up
i not sure if that will work either...but i m not so good with isomorphic
i usually make a mistake going there

4. ## 4 regular graph on 6 vertices.

Originally Posted by AwesomeDesiKid
Prove there is precisely one 4 regular graph on 6 vertices.
any advice will help
That will be a graph obtained by removing 3 edges from complete graph on 5 vertices .

proof .
consider 5-regular graph with 6 vertices it is nothing but complete graph on 5 vertices .Now you need to reduce one degree for each of six vertices that is you need to remove 3 edges.

5. ## 4-regular graph with 6 vertices

That will be a graph obtained by removing 3 edges from complete graph on 5 vertices .

proof .
consider 5-regular graph with 6 vertices it is nothing but complete graph on 5 vertices .Now you need to reduce one degree for each of six vertices that is you need to remove 3 edges.